Paper Citation Record · LEDGER

Are Deep Learning Based Hybrid PDE Solvers Reliable? Why Training Paradigms and Update Strategies Matter

As of 12 August 2026, this Paper Citation Record lists 16 of 16 outbound references and 1 inbound Pith citation observation for arXiv:2602.06842.

A citation records a reference. It does not transfer a finding from one paper to another.

pith.paper-citation-record.v1
2602.06842 v2

Coverage vector

measured 16 of 16 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-03T03:49:46.006008Z

measured 17 of 17 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-12T06:34:41.77262+00:00

measured 1 of 1 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-05-20T01:58:19.874612Z

measured 0 of 1 external citation measurements

A source-named dated measurement, never combined with another source.

Source: arxiv_reference, observed 2026-07-10T12:15:01.137692Z

Reference resolution

16 of 16 outbound references displayed

verified exact0
verified fuzzy0
unresolved16
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 397ca113-fb91-4443-8710-1b3353061f69 · outbound

This paper cites Number 13.

Are Deep Learning Based Hybrid PDE Solvers Reliable? Why Training Paradigms and Update Strategies Matter Number 13

Reference 1

Resolution: unresolved; no resolver link, observed 2026-08-03T03:49:43.755283Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation a26f6ecf-dbf0-49f4-9671-1af714b62be4 · outbound

This paper cites Preconditioning techniques for large linear systems: a survey.Journal of computational Physics, 182(2):418–477, 2002.

Are Deep Learning Based Hybrid PDE Solvers Reliable? Why Training Paradigms and Update Strategies Matter Preconditioning techniques for large linear systems: a survey.Journal of computational Physics, 182(2):418–477, 2002

Reference 2

Resolution: unresolved; no resolver link, observed 2026-08-03T03:49:43.888193Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation fff24c12-cd0a-4bc5-bd76-a61906684ca0 · outbound

This paper cites Oosterlee, and Anton Schuller.Multigrid.

Are Deep Learning Based Hybrid PDE Solvers Reliable? Why Training Paradigms and Update Strategies Matter Oosterlee, and Anton Schuller.Multigrid

Reference 3

Resolution: unresolved; no resolver link, observed 2026-08-03T03:49:43.979060Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 54600fb4-de8e-4c33-b09f-ee658732a905 · outbound

This paper cites SIAM, 2015.

Are Deep Learning Based Hybrid PDE Solvers Reliable? Why Training Paradigms and Update Strategies Matter SIAM, 2015

Reference 4

Resolution: unresolved; no resolver link, observed 2026-08-03T03:49:44.151983Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation cada1f90-d63a-464d-bf67-9deec3e7f15f · outbound

This paper cites Chebyshev semi-iterative methods, successive over- relaxation iterative methods, and second order Richardson iterative methods.Numerische Mathematik, 3(1):157–168, 1961.

Are Deep Learning Based Hybrid PDE Solvers Reliable? Why Training Paradigms and Update Strategies Matter Chebyshev semi-iterative methods, successive over- relaxation iterative methods, and second order Richardson iterative methods.Numerische Mathematik, 3(1):157–168, 1961

Reference 5

Resolution: unresolved; no resolver link, observed 2026-08-03T03:49:44.349458Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 816377cd-780a-47f8-a1bd-156615520e38 · outbound

This paper cites Anderson acceleration for fixed-point iterations.SIAM Journal on Numerical Analysis, 49(4):1715–1735, 2011.

Are Deep Learning Based Hybrid PDE Solvers Reliable? Why Training Paradigms and Update Strategies Matter Anderson acceleration for fixed-point iterations.SIAM Journal on Numerical Analysis, 49(4):1715–1735, 2011

Reference 6

Resolution: unresolved; no resolver link, observed 2026-08-03T03:49:44.520058Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation df19c1d3-e6bf-4a92-8504-593130f0942e · outbound

This paper cites an unresolved cited work.

Are Deep Learning Based Hybrid PDE Solvers Reliable? Why Training Paradigms and Update Strategies Matter Unresolved cited work

Reference 7

Resolution: unresolved; no resolver link, observed 2026-08-03T03:49:44.698066Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 5ff19f6c-6bae-4fc6-9548-b12200b8ec2f · outbound

This paper cites Fourier Neural Operator for Parametric Partial Differential Equations.

Are Deep Learning Based Hybrid PDE Solvers Reliable? Why Training Paradigms and Update Strategies Matter Fourier Neural Operator for Parametric Partial Differential Equations

Reference 8

Resolution: unresolved; no resolver link, observed 2026-08-03T03:49:44.826404Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 78bf22e1-b9a4-45e8-a809-f0fc281cc592 · outbound

This paper cites Learn- ing nonlinear operators via DeepONet based on the universal approximation theorem of operators.Nature machine intelligence, 3(3):218–229, 2021.

Are Deep Learning Based Hybrid PDE Solvers Reliable? Why Training Paradigms and Update Strategies Matter Learn- ing nonlinear operators via DeepONet based on the universal approximation theorem of operators.Nature machine intelligence, 3(3):218–229, 2021

Reference 9

Resolution: unresolved; no resolver link, observed 2026-08-03T03:49:44.974081Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 9442ea32-4eb9-461b-945b-7e442e0fc828 · outbound

This paper cites On the Spectral Bias of Neural Networks.

Are Deep Learning Based Hybrid PDE Solvers Reliable? Why Training Paradigms and Update Strategies Matter On the Spectral Bias of Neural Networks

Reference 10

Resolution: unresolved; no resolver link, observed 2026-08-03T03:49:45.123047Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 6c597bef-cb79-4a2f-9cf0-165f92625067 · outbound

This paper cites Blending neural operators and relaxation methods in PDE numerical solvers.Nature Machine Intelligence, pages 1–11, 2024.

Are Deep Learning Based Hybrid PDE Solvers Reliable? Why Training Paradigms and Update Strategies Matter Blending neural operators and relaxation methods in PDE numerical solvers.Nature Machine Intelligence, pages 1–11, 2024

Reference 11

Resolution: unresolved; no resolver link, observed 2026-08-03T03:49:45.313012Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 7b99d717-cd2c-46be-816d-6578ea55332c · outbound

This paper cites A hybrid iterative method based on mionet for PDEs: Theory and numerical examples.Mathematics of Computation, 2025.

Are Deep Learning Based Hybrid PDE Solvers Reliable? Why Training Paradigms and Update Strategies Matter A hybrid iterative method based on mionet for PDEs: Theory and numerical examples.Mathematics of Computation, 2025

Reference 12

Resolution: unresolved; no resolver link, observed 2026-08-03T03:49:45.418518Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 8933cd1f-786c-4d22-b42f-b6269ab53d60 · outbound

This paper cites MIONet: Learning multiple-input operators via tensor product.SIAM Journal on Scientific Computing, 44(6):A3490–A3514, 2022.

Are Deep Learning Based Hybrid PDE Solvers Reliable? Why Training Paradigms and Update Strategies Matter MIONet: Learning multiple-input operators via tensor product.SIAM Journal on Scientific Computing, 44(6):A3490–A3514, 2022

Reference 13

Resolution: unresolved; no resolver link, observed 2026-08-03T03:49:45.557331Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation ae7d1a6d-5f32-4390-a288-4b129be03a41 · outbound

This paper cites Learning singularity-encoded Green’s functions with application to iterative methods.arXiv preprint arXiv:2509.11580, 2025.

Are Deep Learning Based Hybrid PDE Solvers Reliable? Why Training Paradigms and Update Strategies Matter Learning singularity-encoded Green’s functions with application to iterative methods.arXiv preprint arXiv:2509.11580, 2025

Reference 14

Resolution: unresolved; no resolver link, observed 2026-08-03T03:49:45.719403Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation af7062b1-c9f1-400c-a0de-fd310c5ee7b7 · outbound

This paper cites A hybrid iterative neural solver based on spectral analysis for parametric PDEs.Journal of Computational Physics, page 114165, 2025.

Are Deep Learning Based Hybrid PDE Solvers Reliable? Why Training Paradigms and Update Strategies Matter A hybrid iterative neural solver based on spectral analysis for parametric PDEs.Journal of Computational Physics, page 114165, 2025

Reference 15

Resolution: unresolved; no resolver link, observed 2026-08-03T03:49:45.884202Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation f2f9c37b-0131-4c20-804d-ce9bb0a1cadd · outbound

This paper cites Deeponet based preconditioning strate- gies for solving parametric linear systems of equations.SIAM Journal on Scientific Com- puting, 47(1):C151–C181, 2025.

Are Deep Learning Based Hybrid PDE Solvers Reliable? Why Training Paradigms and Update Strategies Matter Deeponet based preconditioning strate- gies for solving parametric linear systems of equations.SIAM Journal on Scientific Com- puting, 47(1):C151–C181, 2025

Reference 16

Resolution: unresolved; no resolver link, observed 2026-08-03T03:49:46.006008Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Pith citing papers

Observation 54c9ffd7-aa1c-421c-bbb1-f0106b5de4de · inbound

When can a neural operator replace a coarse solve? Architectural principles for two-level preconditioning cites this paper.

When can a neural operator replace a coarse solve? Architectural principles for two-level preconditioning Are Deep Learning Based Hybrid PDE Solvers Reliable? Why Training Paradigms and Update Strategies Matter

Reference 55

Resolution: verified exact; arxiv_id, observed 2026-06-03T02:05:45.543805Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.